Question: William is 2 times as old as Luis. Twelve years ago, William was 6 times as old as Luis. How old is Luis now?
Explanation: We can use the given information to write down two equations that describe the ages of William and Luis. Let William's current age be $w$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $w = 2l$ Twelve years ago, William was $w - 12$ years old, and Luis was $l - 12$ years old. The information in the second sentence can be expressed in the following equation: $w - 12 = 6(l - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = 2l$ . Substituting this into our second equation, we get: $2l$ $-$ $12 = 6(l - 12)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $2 l - 12 = 6 l - 72$ Solving for $l$ , we get: $4 l = 60.$ $l = 15$.